On long routes with a screw belay at each station the number of screws go up.  I usually carry 17cm screws for running pro and a 22 or two for belays.  I find that the 17cm are a good compromise for running pro as they are faster to place and have decent holding power in good ice.  The 22's are also good for nice deep v-thread rappel anchors. 
  
I have used the BD Ice Clipper and a Trango Ice Screw racking device.  The BD seems better.  I place 3-4 screws on the clipper, 3-4 on a biner on a shoulder sling. The rest on biners on my harness.  Runners, draws, screamers and such go on the shoulder sling.  This allows access to the gear with both hands.  If I were to rack all my screws on one side, on the clipper, left hand placements would suck. 
  
I have used this system for a number of years and it works well.  But YMMV.